System and methods for T1-based logging

ABSTRACT

System and methods for using nuclear magnetic resonance (MR) T 1  measurements for wireline, LWD and MWD applications and down-hole NMR fluid analyzers. The T 1  measurements are characterized by insensitivity to motion, as the detrimental effects arising from tool motion or fluid flow are effectively reduced or eliminated. T 1  measurements alone or in combination with other standard oil field measurements are shown to provide efficient data acquisition resulting in compact and robust data sets, the potential for substantially increased logging speeds, and simple methods for fluid typing, including direct and robust identification of gas.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application is a division of U.S. patent application Ser.No. 11/731,121, filed on Mar. 29, 2007 now U.S. Pat. No. 7,501,818,which is a division of U.S. patent application Ser. No. 10/957,406,filed on Oct. 1, 2004 now U.S. Pat. No. 7,199,580, which claims thebenefit of the Oct. 3, 2003 filing date of U.S. provisional patentapplication No. 60/508,442.

FIELD OF THE INVENTION

The present invention relates generally to nuclear magnetic resonance(NMR) well logging and in particular to T₁ relaxation measurements forwireline, logging-while-drilling (LWD) and other applications.

BACKGROUND OF THE INVENTION

In oil and gas exploration it is desirable to understand the structureand properties of the geological formation surrounding a borehole, inorder to determine if the formation contains hydrocarbon resources (oiland/or gas), to estimate the amount and producibility of hydrocarboncontained in the formation, and to evaluate the best options forcompleting the well in production. A significant aid in this evaluationis the use of wireline logging and/or logging-while-drilling (LWD) ormeasurement-while-drilling (MWD) measurements of the formationsurrounding the borehole (referred to collectively as “logs” or “logmeasurements”). Typically, one or more logging tools are lowered intothe borehole and the tool readings or measurement logs are recorded asthe tools traverse the borehole. These measurement logs are used toinfer the desired formation properties.

NMR logging has become very important for purposes of formationevaluation and is one of the preferred methods for determining formationparameters because of its non-destructive character. Improvements in theNMR logging tools, as well as advances in data analysis andinterpretation allow log analysts to generate detailed reservoirdescription reports, including clay-bound and capillary-bound relatedporosity, estimates of the amounts of bound and free fluids, fluid types(i.e., oil, gas and water), permeability and other properties ofinterest. In general, NMR logging devices may be separate from thedrilling apparatus (in what is known as wireline logging), or they maybe lowered into the borehole along with the drilling apparatus, enablingNMR measurement while drilling is taking place. The latter types oftools are known in the art as logging-while-drilling (LWD) ormeasurement-while-drilling (MWD) logging tools

NMR tools used in practical applications include, for example, thecentralized MRIL® tool made by NUMAR Corporation, a Halliburton company,and the sidewall CMR tool made by Schlumberger. The MRIL® tool isdescribed, for example, in U.S. Pat. No. 4,710,713 to Taicher et al. andin various other publications including: “Spin Echo Magnetic ResonanceLogging: Porosity and Free Fluid Index Determination,” by Miller,Paltiel, Gillen, Granot and Bouton, SPE 20561, 65th Annual TechnicalConference of the SPE, New Orleans, La., Sep. 23-26, 1990; “Improved LogQuality With a Dual-Frequency Pulsed NMR Tool,” by Chandler, Drack,Miller and Prammer, SPE 28365, 69th Annual Technical Conference of theSPE, New Orleans, La., Sep. 25-28, 1994. Certain details of thestructure and the use of the MRIL® tool, as well as the interpretationof various measurement parameters are also discussed in U.S. Pat. Nos.4,717,876; 4,717,877; 4,717,878; 5,212,447; 5,280,243; 5,309,098;5,412,320; 5,517,115, 5,557,200; 5,696,448; 5,936,405; 6,005,389;6,023,164; 6,051,973; 6,107,796; 6,111,408; 6,242,913; 6,255,819;6,268,726; 6,362,619; 6,512,371; 6,525,534; 6,531,868; 6,541,969;6,577,125 and 6,583,621. The structure and operation of the SchlumbergerCMR tool is described, for example, in U.S. Pat. Nos. 4,939,648;5,055,787 and 5,055,788 and further in “Novel NMR Apparatus forInvestigating an External Sample,” by Kleinberg, Sezginer and Griffin,J. Magn. Reson. 97, 466-485, 1992; and “An Improved NMR Tool Design forFaster Logging,” D. McKeon et al., SPWLA 40th Annual Logging Symposium,May-June 1999. The content of the above patents is hereby expresslyincorporated by reference for all purposes, and all non-patentreferences are incorporated by reference for background.

NMR logging is based on the observation that when an assembly ofmagnetic moments, such as those of hydrogen nuclei, are exposed to astatic magnetic field, they tend to align along the direction of themagnetic field, resulting in bulk magnetization. The rate at whichequilibrium is established in such bulk magnetization is characterizedby the parameter T₁, known as the spin-lattice relaxation time. The T₁parameter characterizes the coupling of nuclear spins toenergy-absorbing molecular motions like rotation, vibration andtranslation.

Another related and frequently used NMR logging parameter is thespin-spin relaxation time T₂ (also known as transverse relaxation time),which is an expression of the relaxation due to non-homogeneities in thelocal magnetic field over the sensing volume of the logging tool. Ingeneral, the mechanisms for spin-spin relaxation time T₂ include, inaddition to those contributing to T₁, the exchange of energy betweenspins. Both the T₁ and the T₂ relaxation times provide information aboutformation porosity, composition and quantity of formation fluid, andother parameters important in oil exploration.

The pioneers in NMR measurement technologies envisioned the relaxationtime T₁ as the primary measurement result because it carries onlyinformation about the liquid-solid surface relaxation and bulk-fluidrelaxation. In particular, unlike the transverse relaxation time T₂, thespin lattice relaxation parameter T₁ is not affected by rock-internalmagnetic field gradients or by differences in fluid diffusivity.Moreover, instrument artifacts influence T₁ measurements to a muchlesser degree than T₂ measurements.

Despite this understanding, modern pulsed NMR logging in the early 1990swas based primarily on T₂ measurements, largely because of hardwarelimitations. Specifically, the construction of the T₁ recovery curverequires data collected with multiple wait times that range from a fewmilliseconds to several seconds. Acquiring T₁ data using tools thatoperated in single-frequency mode without effective pre-polarization wastoo time-consuming and not feasible. T₂ measurements, on the other hand,were faster and contained information similar to T₁ at low resonancefrequencies. As a result, T₂ CPMG measurements were chosen as the mainmode of tool operation.

One characteristic of NMR logging is that unlike many other loggingmethods the measurements are not instantaneous. Each measurement cycle,including the wait time needed for polarization, can take severalseconds. Frequently, several cycles have to be stacked to achieveadequate signal-to-noise ratio (SNR).

Thus, if a cycle takes T seconds to complete, and N cycles must bestacked, the vertical resolution of a measurement is inverselyproportional to vNT, where v is the logging speed. Clearly, the longerthe cycle times and the higher the logging speeds, the worse thevertical resolution. Therefore, an ever-present challenge in NMR loggingis to design tools that can log faster, while retaining acceptablevertical resolution. For practical reasons overcoming this challenge isa important task. Several innovations towards faster logging have beenput into practice over the past several years.

One such innovation was the introduction of multi-frequency logging inthe early 1990s. The benefit of multi-frequency logging is that thetools acquire data simultaneously over several frequencies, and theadditional SNR available can be used to speed up logging as well as toobtain higher-quality results. The state-of-the-art in multi-frequencylogging is the MRIL®-Prime tool by Numar, a Halliburton Corporation,which currently can operate on 9 frequencies.

Another innovation was the introduction of simultaneous acquisition ofpartially and fully polarized echo trains with different SNR. Propertotal porosity measurements require: (1) a short interecho time T_(e) tosample fast decays, (2) high SNR to reduce the uncertainty in theestimation of fast decays, (3) long sampling time (N_(e)T_(e) whereN_(e) is the number of echoes) for adequate sampling of longer decays.It is practically impossible to achieve all these objectives with aunique wait time T_(w), T_(e) and N_(e) combination; while maintainingacceptable logging speeds and vertical resolution. Therefore, onesolution is to optimize the acquisition by mixing partially and fullyrecovered data with different measurement parameters T_(w), T_(e), N_(e)and desired SNR. Another closely related innovation was the concept ofsimultaneous-inversion, where data acquired with different measurementparameters is inverted simultaneously using forward models that properlyaccount for the differences in fluid NMR properties, acquisitionparameters and noise levels.

Yet another innovation was the use of pre-polarization. In this approachthe cycle time for each measurement is shortened, by placing staticmagnets above the antenna section to realize additional polarizationduring tool motion. Current generation NMR tools generally containpre-polarization sections, allowing overall faster logging. Variousother approaches have been attempted in the art, including the patentslisted above.

The focus of this application is on novel systems and methods for T₁ NMRlogging alone or in combination other logging techniques. As discussedin application Ser. No. 60/474,747, filed on May 03, 2003, to the sameassignee as the present application, T₁ logging adds a differentdimension to interpretation, sometimes by complementing T₂ logs,sometimes uniquely by itself. The '747 application is incorporatedherein for all purposes. The novel technical approaches in accordancewith the present invention directed to overcoming problems associatedwith the prior art are discussed below.

SUMMARY OF THE INVENTION

In accordance with the present invention systems and methods for usingnuclear magnetic resonance (NMR) T₁ measurements for wireline, LWD andMWD applications and down-hole NMR fluid analyzers are provided. The T₁measurements are characterized by insensitivity to motion, as thedetrimental effects arising from tool motion or fluid flow areeffectively reduced or eliminated. T₁ measurements alone or incombination with other standard oil field measurements are shown toprovide efficient data acquisition resulting in compact and robust datasets, the potential for substantially increased logging speeds, andsimple methods for fluid typing, including direct and robustidentification of gas.

In one aspect, the present application concerns a direct and more robustmethod for identification of gas. The method is particularly applicablein tight reservoirs, where the longest T₁ for the water phase is known apriori. A simple correction for gas is made possible in suchapplications, without having to resort to sophisticated processingtechniques.

In another aspect, this application concerns ability to use NMR logswith short wait times, on the order of 2 to 3 seconds, capable ofdetermine total porosity estimates using a self-sufficient correctionalgorithm that provides compensation for insufficient polarization. Aparticularly important result of this approach is the ability to provideoverall faster logging, due to shorter cycle times, or higher verticalresolution, dependent on the practical application. Thus, in a specificembodiment using pre-polarization of the NMR logging tool, good verticalresolution can be provided at logging speeds about or higher than 15feet per minute.

In particular, in one aspect the invention is directed to a method foridentifying gas in a geologic formation, comprising the steps of:providing a distribution of nuclear magnetic resonance (NMR) T₁relaxation times corresponding to a NMR log of the geologic formation;selecting a threshold value in the provided T₁ distribution; andintegrating the T₁ distribution above the selected threshold value toobtain an estimate of gas-filled porosity in the geologic formation.

In another aspect, this application is directed to novel combinations ofT₁ and T₂ logs, for example, to estimate the diffusivity of lowviscosity light hydrocarbon (non wetting phase), and combine the abovediffusivity estimates to calculate viscosity, and combine the T₁ and D)values to estimate gas to oil ratios (GOR).

In yet another aspect, the invention is directed to providing acorrection for insufficient polarization of NMR T₁ and T₂ logs basedsolely on a distribution of NMR T₁ relaxation times and acquisitionparameters of the NMR log. In another aspect, the invention is directedto increased-speed T₁ logging, based on corrections for pre-polarizationmagnetization.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects and many attendant features of this invention will beappreciated and better understood with reference to the followingdetailed description when considered in connection with the accompanyingdrawings, wherein:

FIG. 1 is a block diagram of a NMR logging system, which can beprogrammed for use in accordance with a specific embodiment of thepresent invention;

FIG. 2 is a partially schematic, partially block diagram of a NMRlogging tool and attached electronics used in one embodiment directed towireline logging;

FIGS. 3 and 4 illustrate pulse sequences that can be used in specificembodiments of the present invention;

FIGS. 5 and 6 show T₁ and T₂ logs in a tight gas reservoir to illustrateadvantages of T₁ logging in accordance with this invention;

FIG. 7 is a T₁ model illustrating insufficient polarization and thepost-inversion correction method in accordance with one embodiment ofthe present invention; FIG. 8 illustrates the first echo amplitude fromthe longest wait time as a function of depth; FIG. 9 shows porosityphenomena due to insufficient polarization;

FIG. 10 is shows apparent porosity, where the polarization factors havebeen corrected for the longest wait times; the results of post-inversioncorrection in accordance with this invention, applied to the logs shownin FIG. 10 are shown in FIG. 11;

FIG. 12 illustrates polarization profiles used for faster T₁ logging inaccordance with one aspect of the present invention;

FIG. 13 shows porosity logs verifying the quality of petrophysicaldeterminations from T₁ measurements by comparison to corresponding T₂logs in simulated-drilling mode;

FIG. 14 illustrates a series of wireline T₁ logs used to assess theoperational and petrophysical feasibility of the novel approaches inaccordance with the invention;

FIG. 15 shows NMR spectra from two core plugs

FIG. 16 shows the pressure data in a well, confirming the NMR-basedinterpretation in accordance with the present invention;

FIG. 17 shows estimation of gas to oil ratio (GOR) in accordance withthe present invention.

DETAILED DESCRIPTION

Theoretical Background

The first step in any NMR measurement is to align the magnetic nucleiwith a magnetic field. This alignment process, or polarization, is notinstantaneous and takes some time, which is associated with the T₁parameter. In reservoir rocks, the value of T₁ depends on thecharacteristics of the fluids and the confining pore space. Two distinctrelaxation mechanisms acting in parallel determine the longitudinalrelaxation time:

$\begin{matrix}{\frac{1}{T_{1}} = {\frac{1}{T_{1\; B}} + \frac{1}{T_{1\; S}}}} & (1)\end{matrix}$where the subscripts B and S correspond to bulk and surface relaxation,respectively.

Direct measurement of the longitudinal magnetization is not feasible andtherefore requires tipping of the spins onto the transverse plane.Relaxation in the transverse plane is generally a more complex processcompared to T₁ relaxation. In general, the transverse relaxation time T₂is equal to or shorter than its longitudinal counterpart T₁. This ismostly due to molecular diffusion characterized by T_(2D), resulting inthe following equation for the measured T₂ response:

$\begin{matrix}{\frac{1}{T_{2}} = {\frac{1}{T_{2B}} + \frac{1}{T_{2S}} + \frac{1}{T_{2D}}}} & (2)\end{matrix}$where the extra term containing the subscript D corresponds todiffusion. Given the typical magnetic field gradients of modern loggingtools, diffusion can dominate transverse relaxation in the case ofhighly diffusive fluids, leading to large T₁/T₂ ratios.

Tipping of the spins onto the transverse plane is accomplished throughthe application of an RF-pulse at a specific resonance frequency (Larmorfrequency). Once in the transverse plane, the tipped protons induce arapidly decaying signal in the receiver coils of the NMR device. Thetime constant associated with this so-called Free Induction Decay (FID)is on the order of a few tens of microseconds only, making it hard tomeasure directly. Laboratory measurements that aim at quantifying T₁through Saturation Recovery (SR) or Inversion Recovery (IR), oftenmeasure (the amplitude of) this FID. FID measurements have yet to bedemonstrated in oil-field logging tools; measurement of T₁ or T₂ in thefield is usually achieved through a series of spin-echo sequences. Thebest known spin-echo sequence is by Carr, Purcell, Meiboom and Gill(CPMG) and has been developed to facilitate easy measurement of thetransverse relaxation time T₂.

Although Inversion Recovery is the most popular T₁ measurement method inlaboratory applications, Saturation Recovery technique is the practicalchoice in well logging due to its efficiency and shorter cycle times.The SR sequence used for wireline T₁ logging can be considered as aseries of CPMG echo trainlets, comprised of a few echoes with distinctlydifferent wait times. Within this analogy, the signal from the jth echoof the ith wait time, given relaxation times T_(1k) and T_(2k) withassociated amplitudes ak, is given by

$\begin{matrix}{y_{ij} = {\sum\limits_{k = 1}^{K}\;{{a_{k}\left( {1 - {\mathbb{e}}^{{- T_{wi}}/T_{1k}}} \right)}{\mathbb{e}}^{{- j}\;{T_{e}/T_{2k}}}}}} & (3)\end{matrix}$where Te is the inter-echo time. Note that the response y_(ij) isdependent on both T₁ and T₂, and the imprint of T₂ is eliminated whenj=0. In practice, the decoupling of the T₂ response is accomplished byusing very short Te, and only a few echoes. Proper sampling in T₁acquisition requires at least a couple of recovery measurements perdecade. As a rule of thumb, components faster than the shortest recoverytime, or components slower than the longest recovery time can not beresolved. In the example logs shown below, the wait times vary from 10ms to 6.3 s. The shortest inter-echo time is either 0.51 ms, or 0.60 ms.A maximum of 10 echoes are acquired within each trainlet.

T₁ inversion used here is cast as a classic linear least squaresproblem, where the minimum of an objective function is sought, asdescribed below. By defining the residual or the misfit between the dataand the fit by

$\begin{matrix}{{ɛ_{ij} = {d_{ij} - y_{ij}}}{where}} & \left( {4A} \right) \\{y_{ij} = {\sum\limits_{k = 1}\;{{x_{k}\left( {1 - {\mathbb{e}}^{{- {Tw}_{t}}/T_{1k}}} \right)}{\mathbb{e}}^{{- j}\;{T_{e}/T_{2k}}}}}} & \left( {4B} \right)\end{matrix}$and d_(ij) is the amplitude of the jth echo in the ith CPMG trainlet,the objective function to be minimized to determine that unknown vectorx is given by

$\begin{matrix}{{\Phi(x)} = {{\sum\limits_{i = 1}^{I}\;{\sum\limits_{j = 1}^{J}\; ɛ_{ij}^{2}}} + {\alpha{\sum\limits_{k = 1}^{K}\; x^{2}}}}} & (5)\end{matrix}$

Note that the elements of the unknown vector x contain the amplitudes ofthe T₁ distribution. While the first term in the objective functionrepresents the sum of the squares of the misfit, the second termrepresents the penalty, or the regularization term that is applied toprevent spiky or oscillatory distributions. Zeroth order regularizationhas been used in the above equation only for sake of simplicity, sincemany alternatives exist for regularization. It should be noted here thatas part of solving the linear problem, the relaxation times T_(1k) andT_(2k) are determined apriori. However, the longitudinal and transverserelaxation times can not be treated as independent properties since ingeneralT _(2k)=f(T _(1k)),  (6)where the explicit dependence may vary with k. The relationship isgoverned by the relaxivity of the rocks in the case of the wettingphase, and the bulk and diffusivity properties of the fluids in the caseof the non-wetting phase.

Other factors such as internal gradients may also come into play incertain cases. In the simplest approach, one can define a linearrelationship in the following formT _(2k) =T _(1k)/λ  (7)where λ is a constant, referred to as the T₁/T₂ ratio, with a typicalvalue of 1.5 to 3.0. Actually, the first step of the inversion processused here involves the determination of the function that relates T₂ toT₁, using a model where the relationship is allowed to be non-linear.The information obtained from this initial process is then used in theinversion to set T_(2k) for a given T_(1k).

Various techniques for T₁ and T₂ measurements including pulse sequenceshave been developed in the art, including, without limitation, thedisclosures in U.S. Pat. Nos. 5,309,098; 5,517,115, 5,696,448;5,936,405; 6,005,389; 6,023,164; 6,049,205; 6,051,973; 6,107,796;6,111,408; 6,242,913; 6,255,819; 6,268,726; 6,362,619; 6,512,371;6,525,534; 6,531,868; 6,541,969; 6,577,125; 6,600,316, which areincorporated herein for all purposes.

The System and Underlying Measurements

FIG. 1 is a block diagram of a system, which can be programmed for usein accordance with a specific embodiment of the present invention, whichshows individual block components for controlling data collection,processing of the collected data and displaying the measurement results.In FIG. 1 a logging tool 106 comprises an NMR probe controller 30 andpulse echo detection electronics and is lowered in a borehole drilled inthe formation 109. The output signal from the tool detection electronicsis processed by data processor 12 to record NMR pulse echo data from thetool and analyze the relaxation characteristics of the materialssurrounding the borehole. The output of the data processor 12 is fed toparameter estimator 40. Measurement cycle controller 22 provides anappropriate control signals to the probe. The processed data from thelog measurements is stored in data storage 60. Data processor 12 isconnected to display 50, which is capable of providing a graphicaldisplay of one or more measurement parameters, preferably superimposedon display data from data storage 60. The components of the system ofthe present invention shown in FIG. 1 can be implemented in hardware orsoftware, or any combination thereof suitable for practical purposes.

Reference is now made to FIG. 2, which illustrates in a semi-blockdiagram form an NMR logging apparatus, such as the MRIL®-Prime tool ofNumar Corporation (a Halliburton Company), which can be used for NMRmeasurements in accordance with a preferred embodiment of the presentinvention. In standard operation, first portion 6 of the tool isarranged to be lowered into a borehole 7 having a borehole longitudinalaxis 8 in order to examine properties of the geologic formation in thevicinity of borehole 7.

The first portion comprises a generally cylindrical permanent magnet 10,preferably having a longitudinal axis 11, which is preferably coaxialwith the longitudinal axis 8 of the borehole. Alternatively, a pluralityof permanent magnets 10 may be employed. Permanent magnet 10 preferablyhas uniform magnetization substantially perpendicular to thelongitudinal axis of the logging tool, which is parallel to thelongitudinal axis 8 of the borehole 7.

The first portion 6 also comprises one or more coil windings 16, whichpreferably are arranged on top of the permanent magnet and form the toolantenna. The magnetization direction 13 created by the antenna issubstantially perpendicular to the longitudinal axis 11 of the borehole. The coil windings 16, together with a transmitter/receiver (T/R)matching circuit 20 define a transmitter/receiver (T/R) circuit. T/Rmatching circuit 20 typically includes a resonance capacitor, a T/Rswitch and both to-transmitter and to-receiver matching circuitry and iscoupled to a first RF power amplifier 24 and to a receiver pre-amplifier26.

The permanent magnet 10 and coil windings 16 are preferably housed in anon-conductive, non-ferromagnetic protective housing 18. The housing andits contents will hereinafter be referred to as the probe 19. Inoperation, the probe along with RF amplifier 24, preamplifier 26 and T/Rmatching circuit 20, designated collectively as housing 28 are passedthrough the borehole. Alternatively, some of the above elements may belocated above ground in housing 30.

Disposed in a housing indicated in FIG. 2 by block 30, is a controlcircuitry, including a computer 32, which provides a control output to apulse programmer 34. Pulse programmer 34 controls the operation of phaseshifter 44, as well as an RF driver 38, which drives RF power amplifier24. Pulse programmer 34 controls the operation of a variable frequencyRF source 36, the output of which is passed through phase shifter 44 tothe RF driver 38. The signal from RF driver 38 is amplified in RF poweramplifier 24 and passed through T/R matching circuit 20 to the antenna16.

NMR signals from excited nuclei in the formation surrounding theborehole are picked up by the receiving antenna 16 and passed throughT/R matching circuit 20 to RF receiver pre-amplifier 26, the output ofwhich is supplied to an RF receiver 40 which also receives an input fromphase shifter 44. Receiver 40 outputs via an A/D converter with a buffer46 to the computer 32 for providing desired well logging output data forfurther use and analysis.

While the above description was provided with reference to wirelinelogging, it will be apparent that the T₁ measurement principles of thepresent invention in a preferred embodiment can be applied tologging-while-drilling (LWD) or measurement-while-drilling (MWD).Further details on the structure of NMR wireline and LWD tools and fluidanalyzers that can be used in accordance with preferred embodiments ofthe present invention can be found, for example, in U.S. Pat. Nos.4,710,713; 4,717,876; 4,717,877; 4,717,878; 5,280,243; 5,712,566;6,023,164; 6,107,796; 6,111,408; 6,268,726; 6,362,619; 6,512,371;6,525,534; 6,531,868; 6,541,969; 6,577,125 and 6,583,621. Additionaldesigns, as shown in U.S. Pat. Nos. 4,939,648; 5,055,787 and 5,055,788can also be used. As noted earlier, the above patents have beenincorporated herein by reference for all purposes.

In different embodiments, the T₁ and T₂ measurements in accordance withthis invention can be obtained either simultaneously or separately,using the same or different NMR logging tools. In one embodiment, the T₁and T₂ measurements are obtained using the LWD-MWD tool disclosed inU.S. Pat. No. 6,531,868, which has been incorporated by reference. Sucha tool contains two distinct operating modes, one designed forwhile-drilling operations and the other for wiping trips. In oneembodiment, the motion-tolerant T₁ measurements are obtained whendrilling motion is detected and the tool switches over to T₂ oncedrilling ceases. In another embodiment, T₁ and T₂ measurements areacquired simultaneously over the same depth interval during a wipingtrip.

In one embodiment, the process for obtaining T₁ measurements during adrilling operation is described as follows. At the start of ameasurement, one or more radio frequency pulses covering a relativelywide range of frequencies, or using one or more pulses which arefrequency swept, are transmitted to saturate the nuclear magnetizationin a cylindrical volume around the drilling tool. The range offrequencies can be, for example, 50-100 kHz and is covered in a specificembodiment using a rapid succession of short radio frequency pulsessimilar to the first pulse in a standard CPMG pulse sequence, or using asingle long pulse in a frequency sweep. Changing the range offrequencies used in this step varies the position and the width of thesensitive region in the formation. In a specific embodiment using thetool, a frequency range between 50 and 100 kHz saturates the nuclearmagnetization in a cylindrical volume around the tool, where thecylinder has a typical diameter of 14″, a height of 24″, and thicknessof between about 1/2″ to 1″.

Following the step of saturation, which typically takes about 1 ms, inaccordance with the present invention a readout pulse is transmitted ata frequency near the center of the range of covered frequencies. Inalternative embodiments one or more subsequent readout pulses can alsobe used. In accordance with the present invention, a readout pulsesequence is comprised of a 90° pulse followed by data acquisition, or ofa 90° pulse followed by a 180° pulse, followed by data acquisition,where the steps of applying a 180° pulse and data acquisition can berepeated. The readout pulse sequence generally follows a predeterminedwait time, as explained in more detail below. In a specific embodimentthe readout pulse sequence is transmitted at a center frequency of about500 kHz, and is followed by one or more refocusing pulses. Anillustration of a pulse sequence used in a specific embodiment of thepresent invention is shown in FIG. 3. Yet another type of pulse sequencethat can be used in accordance with this invention is illustrated inFIG. 4, as discussed in more detail in the 6,531,868 patent.

Following the readout pulse(s), corresponding NMR echo signals arereceived, amplified and stored for further processing. In accordancewith a preferred embodiment, the amplitude of the retained echo signalis interpreted as the level of nuclear magnetization present after theparticular wait time. In the particular example considered above, thecenter frequency of the NMR echo signals corresponds to about 14″diameter of investigation.

The measurement process described above is repeated for a series ofincreasing wait times the values of which can, for example, be equallydistributed on a logarithmic scale. In a specific embodiment, wait timesare stepped through the values 1 ms, 3 ms, 10 ms, 30 ms, 100 ms, 300 ms,1000 ms and 3000 ms, and the measurement results are stacked to produceseveral data points on a multi-component T₁ relaxation curve. In oneembodiment, only a few echoes are collected for each wait time tocompute the T₁ relaxation curve. Preferably, about two to five echoesper wait time are retained.

T₂ measurements can be obtained either separately or simultaneously withT₁ measurements. In one embodiment, T₂ measurements are obtainedsimultaneously with T₁ measurements during one of the long wait times.This is done by acquiring a large number of echoes, preferably 500,during the long wait time and then using the large number of echoes tocompute the T₂ relaxation curve.

The T₁ and T₂ measurements obtained during the drilling operation areprocessed to derive petrophysical properties of local geologicalformations. As known in the art, these measurements can be used tocompute distributions of T₁ and T₂ relaxation times. The resultantdistributions of T₁ and T₂ relaxation times comprise data points of T₁and T₂ relaxation curves. These relaxation curves are further processedto extract the dominant T₁ and T₂ relaxation modes, from which amountsof bound water, free water and hydrocarbons are estimated. Thecharacteristic T₁ or T₂ times of the surface-wetting phase can also beused to estimate formation pore size distributions and formationpermeability, as known in the art.

In a particular application, the T₁ and T₂ relaxation curves can be usedto determine different pore systems residing in carbonate formations anddetect the existence of diffusive coupling among different pore systems.In one embodiment, a T₁ relaxation curve is obtained and porosityanalysis is performed by observing the T₁ relaxation curve. The T₁relaxation curve may contain one or more peaks or modes. As known in theart, each peak or mode is associated with a pore system in the formationbeing analyzed. The size of each pore system can also be estimated basedon the relaxation time associated with each peak. For carbonateformations, the T₁ relaxation curve is bi-modal, indicating theexistence of both a micro and macro pore systems. Additional details ofthis embodiment are disclosed in application Ser. No. 60/474,747, filedon May 3, 2003, which is incorporated herein by reference.

Applications

Direct Identification of Gas

It is known in the art that methane and more generally gas in theformation has long T₁ and, given the gradient of the NMR logging tools,a short T₂ value, because of its large diffusivity. This observation canbe exploited in the detection of gas in the form of a large T₁/T₂ ratio.Methods, such as the differential spectrum method or time domainanalysis (TDA), have been designed and used to detect and correct gas bymaking use of the T₁ and T₂ contrasts. These differential methods have adrawback, however, because they work on the difference of two signals,which difference can be small particularly in those cases where thehydrogen index (HI) is low, the porosity is low, or invasion is deep. Inother words, there are limitations to these approaches, which areimportant in the proper estimation of total porosity using NMR.

In accordance with the present invention, given knowledge of the rockproperties, one can bypass more sophisticated gas identificationtechniques in certain cases, in particular in applications involvingtight gas reservoirs. In a tight gas reservoir, the longest T₁ of 100%water saturated rock is no more than a few hundred milliseconds. The T₁of gas, on the other hand, is typically on the order of several seconds.In other words, in a tight gas reservoir, any signal longer than aboutone second is in all likelihood only due to gas. In accordance with thisinvention, this observation leads to a novel and simple approach for (i)detecting gas and (ii) correcting the apparent porosity value for gaseffects to calculate total porosity. FIGS. 5 and 6 show T₁ and T₂ logsin a tight gas reservoir, which illustrate this approach. There areseven tracks in each figure, where Track 1 shows Gamma Ray, SP, caliper,PE; Track 2 shows Resistivities; Track 3 shows a VDL of T2distributions; Track 4 shows Porosities from the T2 Log; Track 5 showsTime Domain Analysis (TDA), generated from T2 logs; Track 6 showsPorosities from T₁ log; and Track 7 shows the VDL of the T₁distributions. In each figure the zone of interest is marked by twoboxes.

In particular, the zone of interest in FIG. 5 contains sand withresidual-gas. Residual condition implies that most of the gas has beenproduced and the reservoir will produce mostly water and some gas, atleast initially. The resistivity logs indicate that water saturationsare high, confirming the above conclusion. Nevertheless, there is stillsome gas in the reservoir and this has been confirmed by gas in the mudlogs. Notice that time domain analysis (TDA) in Track 5 shows some gas(dark-shaded area). It is important to notice the corresponding signalin the T₁ distribution in Track 7 (even if not very strong because ofresidual conditions in the case). Since the rocks illustrated in thefigure are tight (i.e., have low porosity, low permeability, small poresizes), such long signal in the T₁ distribution is a strong indicationof gas. At the same time, one can see that the T₂ distribution shown inTrack 3 can hardly be interpreted to have gas without the help of TDA.

In FIG. 6, the zone of interest contains no gas, although there areindications in the TDA analysis (Track 5). The gas shown from TDA is notreal—it is probably an artifact of dealing with very low porosities inthe echo differences. The T₁ distribution does not show any gas,especially when compared to FIG. 5. Unlike the section shown in FIG. 5,there were no gas shows in the zone in FIG. 6, confirming theconclusions derived from the T₁ log alone.

Based on the above observations, in accordance with the presentinvention peaks at shorter T₁ times are interpreted as being due towater, peaks at longer times (around three to four seconds) areattributed to gas. Thus, in a preferred embodiment, the uncorrected gasfilled porosity can simply be obtained directly using the T₁distribution. In particular, selecting a cutoff parameter, which in apreferred embodiment is one second, one can integrate the signal underthe T₁ distribution to obtain the uncorrected gas filled porosity.Furthermore, knowing the HI parameter of gas (already established apriori, given temperature and pressure), one can make the HI correctionin the form at a simple scalar multiplication to obtain a value fortotal porosity. HI is defined as the number of hydrogen atoms per unitvolume relative to that of freshwater at standard temperature andpressure (75.degree. F., 15 psi). Thus the HI value for freshwater istaken as 1.0 and values of HI for other fluids are referenced to thisvalue. HI estimates for various fluids, dependent on temperature andpressure conditions, and how such corrections are applied to providemore accurate porosity estimates are known in the art and need not beconsidered in detail. Importantly, the above operations do not involvetaking the difference of signals, and will thus result in more robustdetection since the threshold for detection is much smaller. Also, HIcorrection for gas in accordance with this invention is verystraightforward and can be applied in the field.

Compensating for Insufficient Polarization

Another application of T₁ logging in accordance with the presentinvention is compensation for insufficient polarization. Assuming asingle exponential behavior (which can be generalized for themulti-exponential case), the apparent (or measured) porosity is relatedto the true porosity byφ_(a)=φ_(t) HI(1−e^(−Tw/T1))  (8)where HI is the hydrogen index; Tw is the wait time; T₁ is alongitudinal relaxation time of the fluid; and the subscripts a and trefer to apparent and true, respectively. Given HI=1, measuring the trueporosity requires1−e ^(−Tw/T1)=1  (9)which holds if Tw≈5T_(1max). Satisfying this requirement for allapplications requires explicit knowledge of T_(1max), which is notalways available a priori. The current practice is to use a very longwait time, sufficient for all cases, typically in the order of 10 to 12seconds. Using such a longe wait time in well logging applicationsforces the use of slow logging speeds, so that reasonable verticalresolution can be maintained.

Although the problem is highlighted for T₁ logging here, the same istrue for T₂ logging. It is known in the art to use different approachesto compensate for insufficient polarization. One such approach is to usea short wait time, no more than about 3 seconds, and apply apolarization correction assuming a known value for the T₁/T₂ ratio. Theproblem is that there are no criteria for determining this value—inorder to make the correction properly, one has to know the T₁ spectrum.So, in the prior art case, it translates into a fudge factor oftendetermined by observing other porosities, such as crossplot,unnecessarily complicating the analysis and creating the potential forerroneous readings.

In a preferred embodiment of this invention, if the longest wait time ina T₁ log is not sufficient for full polarization and there is enoughresolution in the T₁ axis, one can make a polarization correction giventhe apparent T₁ spectrum and knowledge of acquisition parameters.

In particular, the signal y_(ij) from the jth echo of the ith wait time,given relaxation times T_(1k) and T_(2k) with associated amplitudesa_(k) is given by:

$\begin{matrix}{{y_{ij} = {\sum\limits_{k = 1}^{K}\;{{a_{k}\left( {1 - {\mathbb{e}}^{{- T_{wi}}/T_{1k}}} \right)}{\mathbb{e}}^{{- j}\;{T_{e}/T_{2k}}}}}},} & (10)\end{matrix}$

where T_(e) is the interecho time. Assuming a single echo acquisitionfrom this point on (for purposes of simplification in the notation,without loss of generality), Eq. (10) can be further simplified to dropany dependence on echo number, resulting in

$\begin{matrix}{y_{i} = {\sum\limits_{k = 1}^{K}\;{{a_{k}\left( {1 - {\mathbb{e}}^{{- T_{wi}}/T_{1k}}} \right)}{{\mathbb{e}}^{{- T_{e}}/T_{2k}}.}}}} & (11)\end{matrix}$

The term in parenthesis is called the polarization factor. The sum ofthe amplitudes a_(k) yields the true porosity:

$\begin{matrix}{\phi_{t} = {\sum\limits_{k = 1}^{K}\;{a_{k}.}}} & (12)\end{matrix}$Considering I wait times and K T₁ components; given the data vector d ofdimensions (I by 1), and the unknown vector x (I by 1) that contains theamplitudes of the T₁ spectrum, the linear system Ax=d is solved usinglinear least squares techniques to obtain x. The elements of the Amatrix (I by K) is given byA(i,k)=(1−e ^(−T) ^(wi) ^(/T) ^(1k) )e ^(−T) ^(e) ^(/T) ^(2k) .  (13)

Note that the relaxation times are fixed a-priori, usually chosen to beequally spaced on a logarithmic grid. Defining T_(1max) as the longestT₁ component in the actual T₁ spectrum of the fluid, T_(wmax) as thelongest wait (recovery) time in the activation (pulse sequence), and theapparent porosity by

${\phi_{a} = {\sum\limits_{k = 1}^{K}\; x_{k}}},$one can see thatφ_(a)<φ₁, if T_(wmax)<αT_(1max),  (14)

where α is equal to 3 for practical purposes, and is assumed equal to 5in theory. The condition in Eq. (14) defines the phenomenon known asinsufficient polarization, which basically means that the apparentporosity will be less than the true porosity, if the longest wait timeis not at least 3 times the longest T₁ present in the sample. Thus, theonly way to prevent insufficient polarization is to keep T_(wmax) verylong, in the order of 12 to 14 seconds. Using such a long wait time isgenerally impractical, since the long cycle time will lead to very slowlogging speeds. In accordance with a preferred embodiment of thisinvention, one approach to overcoming the insufficient polarization atreasonable logging speeds is to keep T_(wmax) close to T_(1max) (i.e.,T_(wmax)˜T_(1max)), and then compensate for the insufficientpolarization via signal processing. In a preferred embodiment,compensation is done in a separate processing step appliedpost-inversion.

FIG. 7 shows a T₁ model illustrating insufficient polarization and thepost-inversion correction method in accordance with one aspect of thisinvention. The porosity log and the T₁ spectrum are shown in the leftand right tracks, respectively. The straight line in the porosity trackshows the input porosity which, as described below, is 20 pu (porosityunits). The other two illustrated curves correspond to irreducible andmicro porosity. These curves are output automatically by the software,but are not of interest in this modeling study. There are 101 hundreddepth points in the model, where the depths range from 4900 ft to 5000ft. At each point, the input spectrum has two spikes, where eachcomponent has an amplitude of 10 pu. While the two components haveconstant amplitudes, their Tis vary with depth. One component starts at10 ms at the top of the log, and increases with depth to 5000 ms. Theother component starts at 5000 ms at the top of the log , and decreasesto 10 ms at the bottom, resulting in a crossing pattern, where adifferent T₁ range is simulated by the model at each depth. Based onthese values, T_(1max)=5000 ms.

Based on the model shown in FIG. 7, synthetic logs were generated using6 wait times ranging from 1 ms to 6300 ms (I=6), and 10 echoes per waittime (J=10) with a Te of 0.5 ms. The acquisition parameters used in thesimulations are identical to those used in the real logs presented inthe rest of the disclosure. Since each component has a porosity of 10pu, the apparent porosity from the T₁ log, after inversion, should be 20pu at each depth. However, given the longest wait time of 6300 ms(T_(wmax)=6300 ms), the apparent porosity will be less than 20 pu due toinsufficient polarization at the top and bottom of the log, since T₁approaches 5000 ms in these end points (T_(1max)=5000 ms). This can bebest seen from the time domain data, as shown in FIG. 8. In FIG. 8, thefirst echo amplitude from the longest wait time is shown as a functionof depth. Also shown as a straight line is the input total porosity of20 pu. The departure from the 20 pu line, at the top and bottom of thelog, is due to insufficient polarization. The curved line indicates theamplitude of the first echo from the longest wait time. The differencebetween the two lines is due to insufficient polarization, approachingalmost 4 pu at the top and bottom of the log. It will be appreciatedthat prevention of insufficient polarization via acquisition wouldrequire at least a T_(wmax) value of 15000 ms, which is impractical.

The synthetic logs were generated using a conventional linear leastsquares algorithm, in particular the MATLAB mathematical softwareprogram, which is well known in the art. There are 41 bins in theinversion algorithm (K=41), ranging from 1 ms to 10000 ms. Second-orderregularization was applied to prevent oscillations in the distributions.As known, regularization may blur the T₁ distributions because while theposition of the peaks and the total area under the curve are generallymaintained, the regularization process tends to spread the energy intoadjacent bins. This may lead to excessive porosity values when the setof time constants T_(1k) used in the inversion contains elements thatare longer than T_(1max). This observation is illustrated in FIG. 9. Thebasis set contains T_(1k) up to 10000 ms, and closer inspection of FIG.9 shows that there are non-zero amplitudes in bins where T_(1k)>5000 ms,even though T_(1max)=5000. Inversion automatically compensates for thelow polarization factors by boosting the amplitudes associated withthese bins.

In accordance with a preferred embodiment, one approach to resolving theissues illustrated in FIG. 9 is to constrain the polarization factors inthe A matrix and apply a post-inversion correction. In this approach,the polarization factors in matrix A, only for the longest wait time,are set to 1, as shown below:(1−e ^(−T) ^(wi) ^(/T) ^(1k) )=1, for i=I.  (15)

This results in reduced porosities, as shown in FIG. 10, because theamplitudes are not overcompensated. One can see that the apparentporosity is less near the top and the bottom of the log in FIG. 10,similar to the trend observed in FIG. 8. The straight line in theporosity track shows the input porosity (20 pu). The other line is theapparent porosity where the polarization factors are set to 1 for thelongest wait time. This results in lower porosity where the T₁s arelong: at the top and bottom of the log.

The post-inversion correction factors c_(k), given the amplitudes x_(k)from inversion, are defined in accordance with one embodiment of thisinvention by:

$\begin{matrix}{{c_{k} = \frac{1}{1 - {\mathbb{e}}^{{- T_{wi}}/T_{1k}}}},{{{where}\mspace{14mu} i} = {I.}}} & (16)\end{matrix}$

The corrected porosity in a preferred embodiment is then given by:

$\begin{matrix}{\phi_{c} = {\sum\limits_{k = 1}^{K}\;{c_{k}{x_{k}.}}}} & (17)\end{matrix}$

The result of the post-inversion correction applied to the logs shown inFIG. 10 are shown in FIG. 11. As before, the straight line in theporosity track shows the input porosity, which is 20 pu. Thesuperimposed line is the post-inversion corrected apparent porosity,obtained in accordance with one aspect of the present invention.Clearly, except in a few points, the corrected apparent porosity agreeswell with the input porosity. The deviations from the trend are notsystematic, and are probably due to local variations in the randomnoise.

A direct benefit of this polarization compensation method applied inaccordance with a preferred embodiment of this invention is thepotential for increased logging speeds, or increased verticalresolution, since the cycle times are shorter and the data collected arecloser spatially. Faster logging applications are considered below.

Faster Logging

NMR logging is relatively slow compared to other open-hole logs. Thus,while some other logging tools are run at speeds exceeding 2500 ft/hr,NMR logs are rarely run faster than 1000 ft/hr, which speeds have beenrealized only recently with the advent of multi-frequency tools such asthe MRIL®-Prime, discussed above. One limiting factor on the loggingspeed is the time it takes for nuclei to polarize. In particular, beforean NMR measurement is taken, sufficient time has to be allowed forpolarization, because insufficient polarization leads tounder-estimation of formation porosity. Accordingly, pre-polarizationhas become another requirement for fast logging. Modern tools such asthe MRIL®-Prime have sufficient pre-polarization that can be utilized inT₂ logging. Coupled with a long wait time in the order of 10 to 14seconds, one can get full polarization in most formations, and this iswhat makes logging speeds of about 1000 ft/hr feasible. However, thereare limitations on how much faster logging can be done without furthermodifications.

To illustrate the problem, consider the spins subjected to the 90°-pulseat the beginning of the measurement that are left out of the sensitivevolume as the tool moves during the course of a typical CPMG pulsesequence. The loss of signal from these spins creates an artifact in theform of additional decay in the NMR signal. The number of the spins thatare left out is proportional to the product of v*t, where v is thelogging speed and t is measurement time. Obviously at faster loggingspeeds, the affect is more pronounced. Another problem associated withfaster T₂ logging is the vertical resolution of the log, which decreasesas the logging speed increases. This is especially true for the case ofthe typical long wait times used in current practice.

Neither of these problems affects T₁ logging significantly, as discussedin this application. Spins being flushed out of the sensitive region isnot a problem since only a few echoes per wait time are acquired in T₁logging, and the effect due to the loss of spins left out of thesensitive volume during this short time period is insignificant. Theresolution is also not a major problem because T₁ measurement cycles aregenerally shorter than their T₂ counterparts.

An issue that has to be addressed in fast T₁ logging applications is themixed polarization profile where magnetization originating frompre-polarization (B₀>0, B₁=0, referred to as pre-pol below) is mixedwith magnetization originating from the standard magnets where theantenna is located (B₀>0, B₁>0, referred to as standard-pol, or juststandard). In order to understand this phenomenon, consider the twopolarization profiles shown in FIG. 12. In this figure, themagnetization distribution in the sensitive volume at the beginning ofthe CPMG measurement, for a 24-inch antenna, is shown for two differentwait times. The formation modeled has a T₁ of 4000 ms, the logging speedis 900 ft/hr, and the wait times are 2 and 12 seconds, from left toright, respectively. The snapshot of magnetization along the length ofthe antenna is taken immediately after the 90 pulse, just before thefirst echo of the CPMG.

The dark color in FIG. 12 corresponds to the pre-pol component ofmagnetization, while the gray-color is associated with standard-pol.Note that in the case of the long wait time (FIG. 1( b)), there is nogray-shaded region, all of the magnetization is due to pre-pol andpolarization is almost 100%. In the case of the shorter wait time, themagnetization originates from both pre-pol and standard. As can be seenfrom the difference of the magnetization levels, while magnetization dueto pre-pol is almost 100%, the standard-pol portion is about 40%. Notethat if the tool logged very slowly, the level of magnetization would beabout 40%, there is excess magnetization (or polarization) due to toolmotion. This poses a problem, because existing models used in inversionin general do not account for pre-polarization contributions.

To illustrate the problem, consider the following hypothetical casewhere the porosity of the formation is 100 pu, T₁ is 4000 ms, and thewait time is 2000 ms. Based on the profiles shown in FIG. 12, theapparent porosity (assuming that the hydrogen index is 1) in this casewould be

$\begin{matrix}{{\phi_{a} = {\phi_{t}*\left( {1 - {\mathbb{e}}^{{- T_{w}}/T_{1}}} \right)}},} \\{{= {100*\left( {1 - {\mathbb{e}}^{- 0.5}} \right)}},} \\{= {39.35.}}\end{matrix}$

The apparent porosity would be similar if the tool were moving veryslowly. However, in the case of fast logging, due to pre-pol, there ismore magnetization, and the apparent porosity is almost 55 pu. This ismuch more than what it is in the stationary case and must be corrected.While the above example illustrates the problem, it also suggests asolution that can be applied in accordance with another aspect of thepresent invention. In particular, with the addition of a speed relatedterm, the relation between apparent and true porosities can be rewrittenasφ_(a)=φ₁*p₀*p_(v),where p₀ and p_(v) correspond to polarization factors for thestationary(v=0), and non-zero logging speed cases, respectively. Notethat by definition,p ₀=1−e ^(−T) ^(w) ^(/T) ¹ .  (18)

Hence, with the addition of p_(v), one can still obtain the trueporosity.

Unlike p₀, which only depends on the wait time and the T₁, thedefinition of p_(v) is more complex since it depends not only on thewait time and the T₁; but also on the specifics of the pre-polarizationand standard magnetic field distributions, and the logging speed. Thevalues for p_(v) can be computed in a preferred embodiment givenknowledge of tool design parameters. Thus, in the hypothetical exampleused above, p_(v)=1.3924, for v=900 ft/hr and T_(w)=2000 ms, T₁=4000 ms.

If the polarization due to pre-pol is explicitly accounted for in theinversion, the complications due to tool motion vanish. Going back tothe linear system defined for the T₁ problem (See, Eq. 13):Ax=d,A(i,k)=(1−e ^(−T) ^(wi) ^(/T) ^(1k) )e ^(−T) ^(v) ^(/T) ^(2k) ,

one can redefine the A matrix for the speed effects as belowA(i,k,v)=p ₀(i,k)p _(v)(i,k,v)e ^(−T) ^(e) ^(/T) ^(2k) ,  (19)where p₀ is defined as in Eq. (18), and the factors dependent on p_(v)can be determined for a particular tool design a-priori using modeling,or through measurements for a particular tool design and acquisitionparameters. Note that the p_(v) terms change depending on the loggingspeed, which changes can be accounted for using the illustration in FIG.12. Solution of the linear system with the modified A matrix in Eq. 19yields the correct porosity.

The advantage of explicitly accounting for pre-polarizationmagnetization is that one does not have to seek 100% polarization, asshown in FIG. 12( b). Since the sources of polarization are accountedfor explicitly, one can resort to shorter wait times (for example amaximum of 3 seconds instead of 12), and thus increase logging speedsignificantly. Use of such wait times shorten the cycle time for the T₁measurement, which helps retain good vertical resolution at high loggingspeeds.

Estimation of Diffusivity and Gas-to-Oil Ratios

Given two T₂ logs, acquired with different Te's to (inter-echo times),one can estimate of diffusivity of light hydrocarbons using therelationship.

$\frac{1}{T_{2,{hc}}} = {\frac{1}{T_{1,{hc}}} + \frac{D_{0,{hc}} \cdot \left( {G.\gamma.{TE}} \right)^{2}}{12}}$as explained in the examples below. In particular, a T₁ log can beconsidered as a T₂ log acquired with an infinitely short T_(e) (nodiffusion effects). Hence, the combination of a T₁ log and a T₂ log canbe used in accordance with the present invention to estimate directlythe diffusivity of the hydrocarbons phase. Furthermore, in anotheraspect of the invention once the diffusivity is estimated, one canestimate the gas to oil ratio (GOR), combining the T₁ value with the D₀value. An illustration is provided in the following section of thedisclosure on Practical Examples.

PRACTICAL EXAMPLES

T₁ versus T₂ Logging

The T₁ inversion used in commercial applications, wireline or LWD, usesgenerally all the data available, which is typically 10 echoes per CPMGtrainlet. Single echo inversion is either limited to qualitativeprocesses, such as the Reconnaissance Mode (described in paper SPE 62981presented at the 2000 SPE conference), or to those very high SNRapplications, such as the MRILab™ tool where SNR is typically in theorder of 200 or better. All the results presented herein, as well asthose presented in previous publications (paper DDD, presented at the43rd Annual Logging Symposium, Osio, Japan; paper SPE 77395 presented atthe 2002 SPE Annual Technical Conference and Exhibition) use 10 echoesper CPMG. The inter-echo time in all these cases is either 0.51 ms or0.6 ms. All papers identified in this paragraph are incorporated hereinby reference for background.

The porosity logs displayed in FIG. 13 verify the quality ofpetrophysical answers from T₁ measurements and demonstrate theirrobustness and repeatability. Data from eight different runs, in thesame well, are presented in this figure including: a wireline MRIL®PrimeT₂ log; an MRIL-WD™ T₁ log acquired while drilling the well; and sixMRIL-WD™ T₁ logs acquired in simulated-drilling mode, where the tool wasrotated while going up or down in the well.

Track 1 in FIG. 13 shows GR, SP and Caliper logs. Track 2 shows thetotal porosity from all runs (xxPTOTxx), whereas Tracks 3 and 4 show theirreducible and micro porosity curves, respectively (xxT2PIRMXxx,xxPMICxx). The prefix T₁ or T₂ is used to distinguish T₁-based curvesfrom T₂-based curves. The main reservoir is between 550 to 610 feet, andis logged in each pass. Some of the passes do not cover the shallowerportions of the well, and some logs terminate above the washout at 620feet. The standard deviation of the total porosity from the T₁ logs is0.94 pu, and the standard deviation of the irreducible fluid porosityfrom the same is 1.06 pu. The excellent repeatability among the T₁ logs,as well as the close agreement with the benchmark MRIL®-Prime T₂ logshould leave no doubt as to the validity and quality of the T₁measurement results. It should be noted also that the comparisons aremade using the more challenging LWD logs, not wireline logs.

Case Study

As part of a pilot study, a series of wireline T₁ logs were run toassess the operational and petrophysical feasibility of this novelapplication. This study was assisted by access to a major core studythat includes NMR T₁ data.

The logs presented here in FIG. 14 are from the very first well in theprogram. This well was drilled with an 8½″ bit using salt-saturated mud,which resulted in a fairly smooth well bore with some washed-out zonesin the non reservoir carbonate section, and only marginal enlargementand mud-cake buildup in the deeper sandstone reservoirs.

A full suite of openhole logs was acquired in tool-push mode includingcaliper, GR, SP, resistivity, density, neutron, acoustic, formationtester (pressures only), and borehole images. A standard MRIL®-Prime™tool was run to acquire a dual wait time T₂ log, followed by a T₁ logover the same interval. Bore hole enlargement is indicated with darkshading, mud-cake build-up by the gray shading. The second track showssix array-resistivity curves at different investigation depths.Breakdown of the MRIL®T₁ porosity in micro (dark gray), irreducible(dark, striped gray) and moveable (light gray) porosity is presented inthe third track. Density porosity is shown as reference. The gray-shadedT₁ spectra are on a log scale from 0.5 ms to 5 s. Track 5 presents thebreakdown of MRIL®T₂ porosity, using the same shadings as before withthe T₂ spectra (gray shading) in the adjacent track.

NMR core data from an offset well were available from an earlier,large-scale laboratory NMR core study. The main objective of this corestudy was to improve NMR log interpretation by establishing fieldspecific parameters for e.g. spectral- and cut-off BVI, permeability,etc. T₁ measurements were already included in the program, inanticipation of future T₁ based applications. The benefits of this corestudy were immediately realized during the interpretation of the well,particularly in the determination of hydrocarbon types.

The basic log panel in FIG. 14 shows the openhole logs, where thereservoir sands start at a depth of about xx100 ft. The main zone ofinterest starts with 90 feet of clean and homogeneous sand, intersected65 ft from the top by a -most likely sealing- tight streak. There areseveral poorer quality wet sands below the main pay zone, followed byanother small pay zone located between xx335 to xx350 ft. The pay zonescan easily be identified from the difference (under call) between theapparent density and NMR (either T₁ or T₂) porosity logs. Note that thesame logs agree very well in the wet zones. Also, note the resistivitylogs show no signs of significant invasion.

The T₁ log exhibits bi-modal distributions in the pay zones, whereas theT₂ logs are generally uni-modal. Also, the comparison of uncorrected T₁and T₂ porosities in the pay zone reveals that the porosity from the T₂log is higher than T₁ porosity. This can be explained by the fact thatthe T₂ log has a longer wait time. The longest recovery time in the T₁log is 6.3 seconds, while the wait time in the T₂ log is 12.0 seconds.Obviously, more polarization occurs in the case of the longer wait timewhen the reservoir fluid has a long TV. Using the rule-of thumb of threetimes the T₁ for full polarization, one can estimate that the T₁ of thehydrocarbon is at least 2.1 seconds.

While a T₁ value longer than 2.1 seconds would be consistent with theexpected hydrocarbon type of dry gas, apparent T₁ porosity (uncorrectedfor hydrogen index or incomplete polarization), and the T₁ distributionsindicate a different fluid, as discussed next.

The T₁ distributions show a very clear bi-modal distribution in the payzones, where the long T₁ peak is centered about 3 seconds. Since such apeak is not observed in the wet zones, this peak can be easilyattributed to the presence of gas. However, using a T₁ cutoff of 1second, and applying gas corrections to the log (i.e., accounting forpartial polarization and factoring in the Hydrogen Index of 0.48 fornatural gas under the pressure and temperature conditions encountered inthis well), results in a porosity that is significantly higher than whathas been observed field wise. Simply put, the signal associated with thelong T₁s in the pay zone can not be attributed to dry gas only. Thereare two possibilities: (1) some of the signal is due to invasion water,(2) the hydrocarbon is not just methane, but contains heavier components(which effectively increases the HI, reduces the HI-correction and hencethe apparent porosity).

NMR spectra from two core plugs that were included in the beforementioned core study, are shown in FIG. 15. These plugs were taken fromthe core from an offset well. They were first cleaned, then saturatedwith water (Sw=100%) and subjected to a series of conventionalpetrophysical measurements, as well as NMR T₁ and T₂. There is clearlyno support for long T₁s in the fully saturated core data: the slowest T₁components relax at a rate much faster than 1 second. This rules outpossibility #1 to reduce the apparent porosity, only leaving thepossibility that we're not dealing with just dry gas, but also withheavier components.

Ruling out the presence of dry gas helps explain the trends observed inthe T₂ log. Analysis of dual wait time (T₂) data shows differentialamplitudes in the pay sands centered on T₂ values of approximately200-300 ms, instead of the 35 ms that would be expected in the case ofgas. This confirms the interpretation that the reservoir fluid is notgas, but a very light hydrocarbon instead. The T₁ and T₂ of thehydrocarbon phase are 3.5 and 0.3 s, respectively. The large T₁/T₂ ratioindicates a large D₀ value, (see the discussion on estimation of D₀ andGOR). Due to the large diffusivity of the hydrocarbon phase, the waterand hydrocarbon signals overlap in the T₂ domain, but are well separatedin T₁ domain. Lack of diffusion effects in the T₁ log actually result ineasier identification of the pay zones for this reservoir.

FIG. 16 displays the pressure data in the well, confirming the NMR-basedinterpretation: the pressure gradient in the pay sand (Group 1; dots inthe top left corner) is established at 0.23 psi/ft, which corresponds toa density of 0.53 g/cm3, indicative of a light hydrocarbon indeed. Whenentering the wet zones, there is a distinct change in the gradient.

The interval xx190-xx270 ft is of poor to non reservoir quality withsome inter-bedded cleaner layers. The sand body starting at xx270 ft isagain of reservoir quality; the NMR logs, however, match thedensity-derived porosity values much closer, indicating a different(mixture of) reservoir fluid. The much weaker differential signalappears again at T₂≈200 ms, suggesting that the reservoir is onlypartially hydrocarbon filled at these depths. Based on the similaritiesin T₁ and T₂ characteristics, the hydrocarbon is thought to be the samelight oil as encountered higher up in the well. Log analysis, usingconventional data in combination with NMR porosity, confirms thisinterpretation and shows an abundance of free water with some pockets ofgas.

The MRIL® T₁ and T₂ data corroborate this interpretation. Sands ofreservoir quality exhibit T₂ peaks well in excess of 50 ms; most centeron 200 ms. Wherever these T₂ peaks occur in combination with thedistinct T₁ peaks of some 2 s, we are dealing with light (high GOR) oil,whereas the other zones are wet.

Estimation of GOR

Under the assumptions that the reservoir is water-wet and that for thehydrocarbon, T_(1,bulk)≈T_(2,bulk), equations 1 and 2 can be combinedand re-written as:

$\begin{matrix}{\frac{1}{T_{2,{hc}}} = {\frac{1}{T_{1,{hc}}} + \frac{D_{0,{hc}} \cdot \left( {G.\gamma.{TE}} \right)^{2}}{12}}} & (20)\end{matrix}$

Stacking the echo-trains (trainlets) over the entire pay-zone, followedby inversion, yields T_(1,hc)≈3.5 s and T2,hc≈300 ms. These values,combined with the tool parameters in eq. (8) indicate that the viscosityof the light oil in this reservoir is on the order of 13×10-5 cm2 /s.Using the correlations by Lo et al. (paper SPE 63217 presented at the2000 SPE Annual Technical Conference and Exhibition, Dallas, Tex.) of T₁relaxation times with diffusivity D₀ and Gas-to-Oil Ratios (GOR),estimates the GOR in this reservoir at≈2500. This solution is indicatedby the solid dot in FIG. 17. Analyzing the sensitivity of this resultwith respect to the parameters derived from the logs (mainly T_(1,hc)and T_(2,hc)) shows that GOR fits in the range 1000-4000, indicated bythe dark-shaded area in FIG. 17. For details on computing the GORestimates the interested reader is directed to Lo et al., paper SPE63217 presented at the 2000 SPE Annual Technical Conference andExhibition, Dallas, Tex., 1-4 Oct., 2000.

Based on the above, it is apparent that T₁ information alone alreadyadds significant value petrophysically and helps delineating thereservoir fluids and establishing fluid contacts. It was furtherdemonstrated that the measurements have excellent robustness andrepeatability, similar to wireline T₂ logs run under comparableconditions. Given field knowledge, T₁ logging can be used very easily torecognize hydrocarbon bearing zones, and simple cutoff techniques can beused to correct for hydrocarbon effects, since the hydrocarbon phase iseasily and directly identified. It was demonstrated that when combinedwith T₂ log(s), T₁ logs can be utilized to determine diffusivity, GORand viscosity at reservoir conditions of (light) hydrocarbons.Importantly, T₁ saturation recovery logs used in accordance with thepresent invention are more compact than CPMG T₂ logs and can run faster,since their total measurement time is generally shorter compared to T₂logging. The combinations discussed above are believed to be asignificant contribution to the art of NMR logging with wide rangingapplications involving virtually all NMR tools, and a broad range ofpractical applications, including both wireline and LWD/MWD.

While the invention has been described with reference to the preferredembodiments, it will be appreciated by those of ordinary skill in theart that modifications can be made to the structure and form of theinvention without departing from its spirit and scope which is definedin the following claims.

Nomenclature

-   D₀=coefficient for molecular self diffusion, 10-5 cm2/s-   G=magnetic field gradient, gauss/cm-   GOR=Gas Oil Ratio, v/v-   GR=Gamma Ray (log)-   HI=Hydrogen Index-   NE=number of echoes in CPMG sequence-   PE=Photo Electric (log)-   S=surface area of pore space, cm2-   SP=Spontaneous Potential (log)-   Te=echo spacing, ms-   T₁=longitudinal relaxation time (distribution), ms-   T₂=transverse relaxation time (distribution), ms-   Tw=recovery time for magnetization to build-up-   V=volume of pore space, cm3-   φ=porosity, p.u.-   γ=gyro magnetic ratio, 2π*4258 Hz/gauss for protons-   ρ=surface relaxivity, cm/ms    References of Potential Interest-   1. Brown, R. J. S., and Gamson, B. W., 1959: “Nuclear Magnetism    Logging,” Society of Petroleum Engineers, presented at the 34th    Annual Fall Meeting, Dallas, Tex., October 4-7.-   2. Timur, A., 1968: “Effective Porosity and Permeability of    Sandstones Investigated Through Nuclear Magnetic Resonance    Principles,” Paper K, SPWLA, presented at the 9th Annual Logging    Symposium, New Orleans, La.-   3. Kenyon W. E., Howard, J. J., Sezginer, A., Straley, C., and    Matteson, A., 1989: “Pore-size Distribution and NMR in Microporous    Cherty Sandstones,” Paper LL, SPWLA, presented at the 30th Annual    Logging Symposium, Denver, Colo.-   4. Prammer, M. G., Akkurt, R., Cherry, R., and Menger, S., 2002: “A    New Direction in Wireline and LWD NMR,” paper DDD, presented at the    43rd Annual Logging Symposium, Osio, Japan.-   5. Prammer, M. G., Drack, E., Goodman, G., Masak, P., Menger, S.,    Morys, M., Zannoni, S., Suddarth, B., and Dudley, J., 2000: “The    Magnetic Resonance While Drilling Tool: Theory and Operation” paper    SPE 62981 presented at the 2000 SPE Annual Technical Conference and    Exhibition, Dallas, Tex., 1-4 October.-   6. Prammer, M. G., Bouton, J., and Masak, P., 2001: “The Downhole    Fluid Analyzer,” paper N, SPWLA, presented at the 42nd Annual    Logging Symposium, Houston, Tex.-   7. Morley, J., Heidler, R., Horkowitz, J., Luong, B., Woodburn, C.,    Poitzsch, M., Borbas, T., and Wendt, B., 2002: “Field Testing of a    New Nuclear Magnetic Resonance Logging While Drilling Tool”, paper    SPE 77477 presented at the 2002 SPE Annual Technical Conference and    Exhibition, San Antonio, Tex., 29 September-2 October.-   8. Appel, M., Radcliffe, N. J., Aadireddy, P., Bonnie, R. J. M., and    Akkurt, R, 2002: “Nuclear Magnetic Resonance While Drilling in the    U.K. Southern North Sea”, paper SPE 77395 presented at the 2002 SPE    Annual Technical Conference and Exhibition, San Antonio, Tex., 29    Sep.-2 Oct., 2002.-   9. Lo, S.-W., Hirasaki, G. J., House, W. V. and Kobayashi, R., 2000:    “Correlations of NMR Relaxation Times with Viscosity, Diffusivity    and Gas/Oil Ratio of Methane/Hydrocarbon Mixtures” paper SPE 63217    presented at the 2000 SPE Annual Technical Conference and    Exhibition, Dallas, Tex., 1-4 October.

1. A method for analyzing geologic formations, comprising the steps of:obtaining a first set of T₁ NMR measurements of the geologic formation;obtaining at least one second set of T₂ NMR measurements of the geologicformation; and processing said first and at least one second sets of NMRmeasurements to derive an estimate of one or more of: diffusivity, gasto oil ratio (GOR) and viscosity at reservoir conditions, wherein theestimate is obtained from the T₁ NMR measurements and the T₂ NMRmeasurements as a function of T_(2,hc), T_(1,hc), G, TE, where G is thegradient of the magnetic field and the T₁ NMR measurements are used toapproximate T₂ NMR measurements with an infinitely short T_(E).
 2. Themethod of claim 1, wherein an estimate of diffusivity is obtained fordiffusivity of low viscosity light hydrocarbons.
 3. The method of claim1, wherein an estimate of diffusivity D₀ is obtained directly from theT₁ NMR measurements and the T₂ NMR measurements using:$\frac{1}{T_{2,{hc}}} = {\frac{1}{T_{1,{hc}}} + \frac{D_{0,{hc}} \cdot \left( {G.\gamma.{TE}} \right)^{2}}{12}}$where G is the gradient of the magnetic field, γ is the gyromagneticratio and the T₁ NMR measurements are considered as being acquired withan infinitely short T_(E).
 4. The method of claim 1, wherein an estimateof GOR is obtained by combining a D₀ estimate and T₁ values.
 5. Themethod of claim 1, further comprising a step of pre-polarizing thegeologic formation.
 6. The method of claim 1, further comprising a stepof compensating for insufficient polarization within the geologicformation.
 7. The method of claim 1, further comprising a step ofdelineating reservoir fluids based on the one or more derived estimate.8. The method of claim 1, further comprising a step of identifyinghydrocarbon bearing zones based on the one or more derived estimate. 9.The method of claim 1, further comprising the step of processing the T₁NMR measurements and an estimate of diffusivity.
 10. The method of claim1, further comprising the step of plotting the T₁ NMR measurements andan estimate of diffusivity.
 11. A system for analyzing geologicformations, comprising: means for obtaining a first set of T₁ NMRmeasurements of the geologic formation; means for obtaining at least onesecond set of T₂ NMR measurements of the geologic formation; and meansfor processing said first and at least one second sets of NMRmeasurements to derive an estimate of one or more of: diffusivity, gasto oil ratio (GOR) and viscosity at reservoir conditions, wherein themeans for processing said first and at least one second sets of NMRmeasurements is configured to derive an estimate from the T₁ NMRmeasurements and the T₂ NMR measurements as a function of T_(2,hc),T_(1,hc), G, TE, where G is the gradient of the magnetic field and theT₁ NMR measurements are used to approximate T₂ NMR measurements with aninfinitely short T_(E).
 12. The system of claim 11, wherein the meansfor processing said first and at least one second sets of NMRmeasurements is configured to derive an estimate of diffusivity fordiffusivity of low viscosity light hydrocarbons.
 13. The system of claim11, wherein the means for processing said first and at least one secondsets of NMR measurements is configured to derive an estimate ofdiffusivity D₀ directly from the T₁ NMR measurements and the T₂NMRmeasurements using:$\frac{1}{T_{2,{hc}}} = {\frac{1}{T_{1,{hc}}} + \frac{D_{0,{hc}} \cdot \left( {G.\gamma.{TE}} \right)^{2}}{12}}$where G is the gradient of the magnetic field, γ is the gyromagneticratio and the T₁ NMR measurements are considered as being acquired withan infinitely short T_(E).
 14. The system of claim 11, wherein the meansfor processing said first and at least one second sets of NMRmeasurements is configured to obtain an estimate of GOR based on a D₀estimate and T₁ values.
 15. The system of claim 11, further comprisingmeans for pre-polarizing the geologic formation.
 16. The system of claim11, wherein the means for processing said first and at least one secondsets of NMR measurements is configured to compensate for insufficientpolarization within the geologic formation.
 17. The method of claim 9,wherein the step of processing the T₁ NMR measurements and the estimateof diffusivity is used to derive formation properties.
 18. The method ofclaim 9, wherein the step of processing the T₁ NMR measurements and theestimate of diffusivity is used to derive fluid properties.
 19. Thesystem of claim 11, further comprising means for processing the T₁ NMRmeasurements and an estimate of diffusivity.
 20. The system of claim 19,wherein the means for processing the T₁ NMR measurements and theestimate of diffusivity is used to derive formation properties.
 21. Thesystem of claim 19, wherein the means for processing the T₁ NMRmeasurements and the estimate of diffusivity is used to derive fluidproperties.
 22. The system of claim 11, further comprising means forplotting the T₁ NMR measurements and an estimate of diffusivity.